Abstracts for talks at the SW MAA meeting,
April 7-8, 2006
Invited Addresses
10:00, Salon A: Richard Thompson, University of Arizona
Title: Discovering New Mathematics While You Teach
Abstract: Mathematics is much more than a collection of theorems and
their proofs. It is a rapidly expanding body of knowledge and thought
patterns that is being done live, and in real time by human beings
called mathematicians. Many new concepts come from extensions of known
results and from new ways of looking at existing topics. Communicating
this to students at all levels is very important. There is no more
compelling way to demonstrate the development of new mathematics than by
thinking “on your feet” in the classroom. I will discuss three examples
of such experiences that came up in one course during a recent semester.
(i) Did Bernoulli know EVERYTHING about Bernoulli’s Inequality? (ii)
Have you ever seen a LOCAL LINEAR APPROXIMATION OF ORDER n? (iii) A computer can
approximate a NONEXISTENT number to 5 decimal places!
I will use computer illustrations for the examples. The talk should be
accessible to anyone who has completed a basic calculus sequence.
10:00, Salon B: Derek Habermas and Erin McNicholas, University of Arizona
Title: Concept Tests
10:00, Salon C: Feryal Alayont, Marilou Mendel, University of Arizona, Joseph Erker, Pima Community College
A panel discussion on Writing in mathematics
Abstract: Incorporating writing into mathematics has many positive outcomes, if
done carefully. In this panel, we will discuss the various ways writing
assignments can be used in mathematics courses at different levels with concrete
examples, how the writing
assignments can be structured to obtain the greatest benefit, and the design of
effective
grading rubrics for writing assignments.
Friday, April 7, 2006
10:50, Salon A: William McCallum and Deborah Hughes Hallett, University of Arizona
Title: Algebraic Manipulation
Abstract: In this workshop-discussion, we will start by considering the questions:
· What is algebra?
· What do our students need?
The students in College Algebra are diverse in backgrounds and interests. Some need to understand data and mathematical models; others need to be able to read and manipulate mathematical formulas. We will concentrate on the needs of the second group, for whom great possibilities are emerging. The workshop will ask participants to consider the categories of problems that encourage students to think critically about algebra. We believe that conceptual understanding is essential to the development of algebraic fluency, and that well-constructed problems can make a major contribution to this. In the workshop, participants will comment on the problem types presented, and have the opportunity to present their own.
10:50, Salon B: Chris Mikel, Coordinator of the Math Center, University of Arizona, will moderate a panel of undergraduate and graduate students on the topic: Mentoring from a student’s perspective.
10:50, Salon C: April Strom, Scottsdale Community College
Title: The Role of Covariational Reasoning in Learning and Understanding
Exponential Functions
Abstract: Understanding the concept of exponential functions and multiplicative
rate of change is critical for students as they progress through mathematics.
Not only are exponential growth and decay topics encountered in our everyday
world, these functions are embedded in the sciences as well as mathematics, and
they provide a model for representing multiplicative growth and decay patterns
for real world phenomena. The National Council of Teachers of Mathematics (NCTM,
2000) and the American Mathematical Association of Two-Year Colleges (AMATYC,
1995) standards advocate for high school and college mathematics curricula to
include the topic of exponential
functions and emphasize the importance of developing this functional
understanding and multiplicative behavior conceptually through the use of real
world contexts. Research has shown that students experience difficulty
developing a profound and robust understanding of exponential functions (Confrey
& Smith, 1995; Weber, 2002). However, irrespective of these findings, more
research is needed to investigate the process of coming to understand
exponential functions. This paper will discuss the role of covariation in
learning exponential functions and in the development of building a
profound, flexible knowledge base of multiplicative structures. Findings from a
study will be discussed on the various ways that high school mathematics and
science teachers use covariation when performing exponential function tasks.
11:40: Salon A: Gabriel Mendoza and Alfredo Rodriguez, El Paso Community College
Title: Tablet PCs and implementation
Abstract: Technology is evolving our world every day. The Tablet PC is revolutionizing how we teach and deliver our lecturing material to our students. Tablet PC’s give us the opportunity to work and project our lectures on to a board for the students to see via an LCD projector. At the end of your lecture, you have the opportunity to distribute these notes by means of email to every student in your class. As one may know Tablet PC’s can be quite expensive, so as a result an alternative to this technology wonder will also be presented. The WACOM Mouse Pen is a device that acts similar to the Tablet PC at a fraction of the cost. At the end of this presentation, we will have a discussion of the benefits and disadvantages of this technology in the classroom.
11:40, Salon B: Mary Sibayan, Pima Community College and Dan Madden, University of Arizona, are organizing the Articulation Task Force.
Friday, April 7, 2006
11:40, Salon C: Adam Stinchcombe, Arizona Eastern College
Title
of talk: The Lagrange Interpolation Polynomial.
Abtract: The Lagrange interpolation polynomial is designed to pass through any
given set of function values. In comparison to least squares, the
Lagrange interpolation polynomial gives R2 = 1 each time. The formula looks
intimidating but one can make sense out of it by seeing how it fits a parabola
through three points. It can be the source of fun explorations in calculus,
especially when supplemented by a CAS. In linear algebra, the Lagrange
interpolation polynomial also suggests an alternate basis for the vector space
of nth degree polynomials.
1:30, Salon A: Frank J. Attanucci, Maricopa Community College
Title: Analyzing the Surface Behavior of the Fluid in a Revolving Container.
ABSTRACT: A container has a bottom that lies in the xy-plane and sides that are
parallel to the z-axis (all lengths measured in meters). The container sits on
a turntable, centered at the origin, which turns about the z-axis at an angular
speed (radians per sec). I investigate the shape of the surface of the fluid
in the spinning container (assuming that the angular speed of the fluid is
everywhere the same as the angular speed of the container and that every point
in the fluid moves in a circular path). Specifically, I derive formulas for the
height of the fluid Z as a function of its radial distance from the axis of
rotation and the angular speed of the turntable, i.e., . I then use these
formulas to find the angular speed needed so that the depth of the fluid (at its
shallowest point) "just reaches" zero and, at this speed, I calculate the
maximum height of the fluid along the side of
the container. In addition to deriving these formulas for fluid height from
relevant
physics principles, I create an animation of the phenomenon using Maple.
Finally, I conduct the experiment in order to confirm that the fluid in one such
spinning container (here, a rectangular parallelepiped) in fact behaves in the
manner predicted by the theory.
1:30, Salon B: Kim Marsden, Pearson Education/Addison Wesley
Title: Taking Homework Integration to the Next Level with MathXL.
1:30, Salon C: Rebecca Hartzler, Edmonds Community College
Rebecca Hartzler will be doing the 1 hour informative session and 2 hour workshop on the MAC^3 program.
Abstract: The Mathematics Across the Community College Curriculum project has influenced over 28 disciplines and two-dozen institutions. Come get inspired about the many mathematics applications that exist in other disciplines and how you can help to make mathematics a welcome and indispensable part of the entire undergraduate curriculum.
2:20, Salon
A:
Janet McShane, Nándor
Sieben and John Hagood, Northern Arizona University
Title: The WeBWorK Homework System: College Mathematics through Linear
Algebra.
Abstract:
During the past two years, our department has implemented the WeBWorK homework
system in a variety of courses, from College Mathematics
through Linear Algebra. As part of this, we have developed problem sets for
College Mathematics, Discrete Mathematics, Finite Mathematics, Precalculus,
Statistics and other courses which are now available as part of the national
problem library on the University of Rochester WeBWorK server. We will give a
brief demonstration of WeBWorK, present data from our use of WeBWorK, and
present some of the contributions of our department to this national project.
Friday, April 7, 2006
2:20, Salon B: Ksenija Simic and Matt Ondrus, University of Arizona
Title: Experiences and reflections of two math post-docs involved in a math education grant:
Abstract: The NSF-funded Center for the Mathematics Education of Latinos/as (CEMELA)[1] is an interdisciplinary, multi-university consortium focused on the research and practice of the teaching and learning of mathematics with Latino students in the United States. CEMELA aims to understand the interplay of mathematics teaching and learning and the language, social, cultural and political issues that affect Latino communities. The Center has been in existence since fall 2004, and the two of us have been involved as fellows since spring 2005. In this talk, we will get the audience better acquainted with CEMELA through the following questions: What is CEMELA, and what are the backgrounds of the people involved? Why did we get involved? What do mathematicians bring to CEMELA and what does CEMELA bring to mathematicians? What do non-mathematicians bring to CEMELA? What (specifically) have we done as part of CEMELA? Who might be interested in becoming part of CEMELA as a graduate student, and how does one become involved?
3:15, Salon A: Shafiu Jibrin, Northern Arizona University
Title: Generating Uniform Points on the Boundary of Bounded Spectrahedron
Abstract: This talk presents algorithms for generating (asymptotically) uniform
points on the boundary of full-dimensional bounded spectrahedron (a closed
convex set defined by set of linear matrix inequality constraints). The
algorithms have a potential application to solving semidefinite programming
problems.
3:15, Salon B: Anne Dudley, Maricopa Community College
Title: Math & Jeopardy (or I have an answer, do you know the question?)
Abstract: Come play Jeopardy with Anne Dudley and reflect on 20 years of
change in mathematics education. Along the way, you will dust the
cobwebs off your memories and laugh about the way things were (and are).
Be careful, you might even learn something you can use in the classroom
on Monday!
4:05, Salon A: Glenn Hurlbert, Arizona State University, Fred Stevenson, and William McCallum, University of Artizona, will lead a panel discussion efforts by mathematics departments to help increase the number of high school mathematics teachers teachers.
4:05, Salon B: Janet M. McShane and Michael I. Ratliff, Northern Arizona University
Title: Pictures at a Regression
Abstract: The overall intention of this talk is to compare various simple regression methods by looking at their graphical performance. The regression methods that we consider are: the least squares method, the least absolute value of errors method, Theile’s complete method, Theile’s incomplete method, and the so-called Med-Med method. We first describe each method, and compare how each method performs on a given data set. We then vary the data sets with respect to the correlation coefficient, and consider how each method responds. Lastly, we append an additional point, (x,y), to our data sets, and look at the graph of the function m(x,y), the slope of the new line of regression, as a function of the point (x,y). These graphs or pictures will give us a sense of how the various regression methods are influenced by adding an additional point to a data set, and from this we can graphically determine the most and least influential points.
Saturday, April 8, 2006
10:00, Salon A: Dorin Dumistriscu, University of Arizona
Title: The Calculus Visitation Project at UA: encouraging high-school students to take more math courses in college
10:00, Salon B: Nick Ercolani and William Y. Velez, University of Arizona, will continue the discussions from the banquet talk concerning how we can all work together to increase the number of our students pursuing degrees in mathematics.
Exhibitors:
We are very grateful for the financial support of the following companies.
Houghton-Mifflin
Brooks/Cole-Thomson Learning
Prentice Hall
Pearson Education/Addison Wesley
John Wiley and Sons Publishers
Mathematical Association of America